TSTP Solution File: SET642+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:07:48 EDT 2024

% Result   : Theorem 0.57s 0.76s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   31 (   8 unt;   0 def)
%            Number of atoms       :  139 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  164 (  56   ~;  42   |;  43   &)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   83 (  59   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f80,plain,
    $false,
    inference(subsumption_resolution,[],[f77,f75]) ).

fof(f75,plain,
    ~ subset(sK0,cross_product(sK1,sK2)),
    inference(unit_resulting_resolution,[],[f48,f62]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X0,relation_type(X1,X2))
      | ~ subset(X0,cross_product(X1,X2)) ),
    inference(subsumption_resolution,[],[f61,f49]) ).

fof(f49,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/tmp/tmp.kKNRWEJk7v/Vampire---4.8_13911',p19) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X0,relation_type(X1,X2))
      | ~ subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f60,f49]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X0,relation_type(X1,X2))
      | ~ subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f51,f49]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X0,relation_type(X1,X2))
      | ~ subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( subset(X0,cross_product(X1,X2))
               => ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.kKNRWEJk7v/Vampire---4.8_13911',p2) ).

fof(f48,plain,
    ~ ilf_type(sK0,relation_type(sK1,sK2)),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( ~ ilf_type(sK0,relation_type(sK1,sK2))
    & subset(sK0,sK3)
    & ilf_type(sK3,relation_type(sK1,sK2))
    & ilf_type(sK2,set_type)
    & ilf_type(sK1,set_type)
    & ilf_type(sK0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f23,f35,f34,f33,f32]) ).

fof(f32,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ ilf_type(X0,relation_type(X1,X2))
                    & subset(X0,X3)
                    & ilf_type(X3,relation_type(X1,X2)) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(sK0,relation_type(X1,X2))
                  & subset(sK0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK0,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ ilf_type(sK0,relation_type(X1,X2))
                & subset(sK0,X3)
                & ilf_type(X3,relation_type(X1,X2)) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ ilf_type(sK0,relation_type(sK1,X2))
              & subset(sK0,X3)
              & ilf_type(X3,relation_type(sK1,X2)) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK1,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ ilf_type(sK0,relation_type(sK1,X2))
            & subset(sK0,X3)
            & ilf_type(X3,relation_type(sK1,X2)) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ~ ilf_type(sK0,relation_type(sK1,sK2))
          & subset(sK0,X3)
          & ilf_type(X3,relation_type(sK1,sK2)) )
      & ilf_type(sK2,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ( ? [X3] :
        ( ~ ilf_type(sK0,relation_type(sK1,sK2))
        & subset(sK0,X3)
        & ilf_type(X3,relation_type(sK1,sK2)) )
   => ( ~ ilf_type(sK0,relation_type(sK1,sK2))
      & subset(sK0,sK3)
      & ilf_type(sK3,relation_type(sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X0,relation_type(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X0,relation_type(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X1,X2))
                   => ( subset(X0,X3)
                     => ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.kKNRWEJk7v/Vampire---4.8_13911',prove_relset_1_4) ).

fof(f77,plain,
    subset(sK0,cross_product(sK1,sK2)),
    inference(unit_resulting_resolution,[],[f47,f46,f65]) ).

fof(f65,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X0,cross_product(X1,X2))
      | ~ subset(X0,X3)
      | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(subsumption_resolution,[],[f64,f49]) ).

fof(f64,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X0,cross_product(X1,X2))
      | ~ subset(X0,X3)
      | ~ ilf_type(X3,relation_type(X1,X2))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f63,f49]) ).

fof(f63,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X0,cross_product(X1,X2))
      | ~ subset(X0,X3)
      | ~ ilf_type(X3,relation_type(X1,X2))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f52,f49]) ).

fof(f52,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X0,cross_product(X1,X2))
      | ~ subset(X0,X3)
      | ~ ilf_type(X3,relation_type(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(X0,cross_product(X1,X2))
                  | ~ subset(X0,X3)
                  | ~ ilf_type(X3,relation_type(X1,X2)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(X0,cross_product(X1,X2))
                  | ~ subset(X0,X3)
                  | ~ ilf_type(X3,relation_type(X1,X2)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => subset(X0,cross_product(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.kKNRWEJk7v/Vampire---4.8_13911',p1) ).

fof(f46,plain,
    ilf_type(sK3,relation_type(sK1,sK2)),
    inference(cnf_transformation,[],[f36]) ).

fof(f47,plain,
    subset(sK0,sK3),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 16:38:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.kKNRWEJk7v/Vampire---4.8_13911
% 0.57/0.75  % (14309)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.75  % (14309)Refutation not found, incomplete strategy% (14309)------------------------------
% 0.57/0.75  % (14309)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (14302)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (14309)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (14309)Memory used [KB]: 1022
% 0.57/0.75  % (14309)Time elapsed: 0.002 s
% 0.57/0.75  % (14309)Instructions burned: 2 (million)
% 0.57/0.75  % (14303)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.75  % (14306)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (14305)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.75  % (14304)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75  % (14307)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.75  % (14309)------------------------------
% 0.57/0.75  % (14309)------------------------------
% 0.57/0.75  % (14308)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.75  % (14307)Refutation not found, incomplete strategy% (14307)------------------------------
% 0.57/0.75  % (14307)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (14307)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (14307)Memory used [KB]: 1022
% 0.57/0.75  % (14307)Time elapsed: 0.003 s
% 0.57/0.75  % (14307)Instructions burned: 2 (million)
% 0.57/0.75  % (14307)------------------------------
% 0.57/0.75  % (14307)------------------------------
% 0.57/0.75  % (14302)Also succeeded, but the first one will report.
% 0.57/0.75  % (14305)First to succeed.
% 0.57/0.76  % (14306)Refutation not found, incomplete strategy% (14306)------------------------------
% 0.57/0.76  % (14306)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76  % (14306)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.76  
% 0.57/0.76  % (14306)Memory used [KB]: 1035
% 0.57/0.76  % (14306)Time elapsed: 0.003 s
% 0.57/0.76  % (14306)Instructions burned: 4 (million)
% 0.57/0.76  % (14306)------------------------------
% 0.57/0.76  % (14306)------------------------------
% 0.57/0.76  % (14308)Also succeeded, but the first one will report.
% 0.57/0.76  % (14305)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14121"
% 0.57/0.76  % (14311)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.57/0.76  % (14305)Refutation found. Thanks to Tanya!
% 0.57/0.76  % SZS status Theorem for Vampire---4
% 0.57/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.76  % (14305)------------------------------
% 0.57/0.76  % (14305)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.76  % (14305)Termination reason: Refutation
% 0.57/0.76  
% 0.57/0.76  % (14305)Memory used [KB]: 1035
% 0.57/0.76  % (14305)Time elapsed: 0.004 s
% 0.57/0.76  % (14305)Instructions burned: 4 (million)
% 0.57/0.76  % (14121)Success in time 0.387 s
% 0.57/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------